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Question
There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:
| C1 | C2 |
| (a) In how many ways committee: can be formed | (i) 10C2 × 19C3 |
| (b) In how many ways a particular: professor is included | (ii) 10C2 × 19C2 |
| (c) In how many ways a particular: lecturer is included | (iii) 9C1 × 20C3 |
| (d) In how many ways a particular: lecturer is excluded | (iv) 10C2 × 20C3 |
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Solution
| C1 | C2 |
| (a) In how many ways committee: can be formed | (i) 10C2 × 20C3 |
| (b) In how many ways a particular: professor is included | (ii) 9C1 × 20C3 |
| (c) In how many ways a particular: lecturer is included | (iii) 10C2 × 19C2 |
| (d) In how many ways a particular: lecturer is excluded | (iv) 10C2 × 19C3 |
Explanation:
(a) We have to select 2 professor out of 10 and 3 lecturers out of 20
∴ Number of ways of selection = 10C2 × 20C3
(b) When a particular professor is included taken the number of ways = `""^(10 – 1)"C"_1` × 20C3
= 9C1 × 20C3
(c) When a particular lecturer is included then number of ways = 10C2 × 19C2
(d) When a particular lecturer is excluded, then number of ways = 10C2 × 19C3
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